Signal distortion in an optical channel may be caused by nonlinearities that exist in various components, which comprise an optical channel. Such distortion can be characterized by mathematical models of the nonlinear behavior of the optical communication channel. By using such models, compensatory measures, for example equalizers that compensate for distortion, which degrades the performance of the channel, may be designed.
One source of distortion is dispersion. Dispersion may be a combination of linear and nonlinear components.
Dispersion found in optical fibers, particularly multimode fibers, may limit the bandwidth in optical channels. The problem of dispersion may be more acute in multimode fibers in general, but it may also be a problem in single mode fibers, especially in long runs of fiber. Single mode fibers commonly have lower dispersion than multimode fiber. The dispersion commonly found in single mode fibers may be chromatic dispersion or polarization mode dispersion. The dispersion that is seen in single mode fibers is generally a lot less per length than the dispersion found in multimode fibers. Dispersion is cumulative, however, and so tends to increase as fibers increase in length. Accordingly, methods discussed herein in terms of multimode fibers may apply equally well to single mode fibers.
In multi-mode fibers, the multiple modes of propagation within the fiber commonly cause dispersion. Generally, in the various modes of propagation within a fiber, the light signal has different speeds of propagation. So if a light pulse is sent from a transmitter, the pulse will propagate in multiple modes traveling at different speeds. The pulse, traveling in each mode, will reach the receiver at a different time. The multiple times of arrival of the input pulse traveling in several modes create a distorted pulse, somewhat like a spread out version of the transmitted pulse.
Optical channels are inherently nonlinear. Electromagnetic fields can be described by Maxwell's equations, which are linear. Because Maxwell's equations are linear, the principle of superposition applies to the electromagnetic field. What is modulated, however, in optical channels is not the electromagnetic field per se, it is the optical power. Superposition doesn't exactly apply to optical power.
An optical photo detector is commonly a square law device. The photodetector responds linearly to the optical power, in fact the photo current generated by a photodetector is commonly a very accurately linear function of the optical power, but the power is a quadratic function of the electromagnetic field, thus creating a source of nonlinearity.
It has been shown that if a laser has a large spectral width, instead of being a very monochromatic laser, the significant spectral width tends to result in a linearization of the channel even considering the effect of the optical power and the square law nature of the photodetector. In other words if a laser has a very monochromatic, narrow spectrum then the channel tends to behave less linearly than does a laser that has a wider spectrum.
Nonlinear behavior in an optical channel may depend to varying extent on the properties of the photodetector and the fiber. Additionally there is a possibility of distortion from the laser itself. If there is dispersion in the laser, for example because the laser has some bandwidth limitation itself, then nonlinearity of the laser could also contribute to the total nonlinearity in the optical channel.
When the intensity of an optical signal is high, a fiber optic which transmits the optical signal itself may introduce nonlinearities. These nonlinearities may result from the fact that the index of refraction of the fiber optic depends, to some extent, on the intensity of the optical signal itself. This effect commonly gives rise to nonlinearities known as “four-wave mixing”, “self-phase modulation”, and “cross-phase modulation”. Additional nonlinearities may result from the phenomena known as stimulated Raman scattering and stimulated Brillouin scattering. For a more comprehensive treatment of nonlinearities, see the text “Fiber-Optic Communication Systems”, second edition, by Govind P. Agrawal, John Wiley and Sons, 1997, ISBN 0-471-17540-4, which is incorporated by reference herein.
Although the above sources of nonlinearity in an optical channel are presented as examples, other sources may exist. The techniques described in this disclosure may be applied to all kinds of nonlinearities regardless of their physical source, as will be clear to those skilled in the art.